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Total: [10 marks) the production function f(x,x)) = Calculate the cost minimising input bundle x1 +...
A firm uses two inputs x1 and x2 to produce output y. The production function is...
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
A firm has decreasing returns production function f(x1, x2)=(x1)1/6(x2) 1/3 and faces input costs w1=1 and...
A firm has decreasing returns production function f(x1, x2)=(x1)1/6(x2) 1/3 and faces input costs w1=1 and w2=2. Find the cost function.
A firm has the production function y= f(x1,x2)= 0.25x11/2 x21/2 . Input prices are w1=$4 and w2=...
A firm has the production function y= f(x1,x2)= 0.25x11/2 x21/2 . Input prices are w1=$4 and w2= $16 a) Use the technical rate of substitution, the input price rate, and the production function to compute the conditionial input demand fucntion x1(y) and x2(y). b) Compute the firm's long run cost function c(y).
Problem 2: A firm has the following production function: f(x1,x2) = x1 + x2 A) Does...
Problem 2: A firm has the following production function: f(x1,x2) = x1 + x2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) Suppose the firm wants to produce exactly y units and that input 1 costs $w1 per unit and input 2 costs $w2 per unit. What are the firm's conditional input demand functions? C) Write down the formula for the firm's total cost function as a function of w1, W2, and y.
A firm uses two inputs x1 and x2 to produce output y. The production function is...
A firm uses two inputs x1 and x2 to produce output y. The production function is f(x1, x2) = x11/2 + x21/2. The price of input 1 is 1 and the price of input 2 is 2. The price of output is 10. (d) Does this production function exhibit increasing, decreasing or constant returns to scale? (e) Solve the firm’s cost minimization problem. Derive the firm’s cost function c(y). (f) Find the profit-maximizing choice of inputs x1* and x2* and...
Consider the following function: where x1 2 0,0,A 0, 0<1. a) Suppose that the preferences of...
Consider the following function: where x1 2 0,0,A 0, 0<1. a) Suppose that the preferences of a consumer regarding the consumption of goods x1 and x2 are represented by function = f(x1,x2) above. Suppose also that the consumer is endowed with some disposable income Y > 0 and faces prices pı and p2 respectively for goods x1 and x2. i) Derive and describe the demand of the consumer for goods x1 and x2. [20 marks] i) Are demand functions affected...
1. Consider the production function f(x1, x2) = 4x 11/2 x 21/3 . What is the...
1. Consider the production function f(x1, x2) = 4x 11/2 x 21/3 . What is the returns to scale? Show your work. 2. What is the TRS for the above production function? 3. What is the optimal level of output that maximizes profit given the output and input prices respectively as p, w1, w2?
iu [5 marks]b ii)) Consider the function, f, as the followings,vRuǐ (x1, x2)-5xỈ + x-. + 4x1 x2-14x1-6x2 + 20 ( !0% x») This function has its optimal solution atx"= (1,1) and f(1, 1) 10. Run t...
iu [5 marks]b ii)) Consider the function, f, as the followings,vRuǐ (x1, x2)-5xỈ + x-. + 4x1 x2-14x1-6x2 + 20 ( !0% x») This function has its optimal solution atx"= (1,1) and f(1, 1) 10. Run the k-th iterates of the Newton algorithm, and compute the descend the k-th iteration (dk). [5 marks] Resource Allocation prob
iu [5 marks]b ii)) Consider the function, f, as the followings,vRuǐ (x1, x2)-5xỈ + x-. + 4x1 x2-14x1-6x2 + 20 ( !0% x») This...
. Discuss about returns to scale of following production function. (a) f(x1, x2) = x a...
. Discuss about returns to scale of following production function. (a) f(x1, x2) = x a 1 +x a 2 b , where a and b are positive constant. (Hint: ab < 1, ab = 1 and ab > 1.) (b) f(x1, x2) = √ x1 + x 2 2 . (Hint: Does it satisfy the definition of increasing return to scale, constant returns to scale, or decreasing returns to scale. How can this be?)
Suppose that Jennifer produces good y by using input xi and x2. The production function which...
Suppose that Jennifer produces good y by using input xi and x2. The production function which Jennifer faces is: y = x} + x3 The cost for every unit of xı is wi and the cost for every unit of x2 is w2. There is a fixed cost component F, which also forms a part of her total cost. (a) Write down the cost minimization problem. Solve this problem and express X1/X2 as a function of w2/w1.
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
A firm has decreasing returns production function f(x1, x2)=(x1)1/6(x2) 1/3 and faces input costs w1=1 and w2=2. Find the cost function.
Problem 2: A firm has the following production function: f(x1,x2) = x1 + x2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) Suppose the firm wants to produce exactly y units and that input 1 costs $w1 per unit and input 2 costs $w2 per unit. What are the firm's conditional input demand functions? C) Write down the formula for the firm's total cost function as a function of w1, W2, and y.
Consider the following function: where x1 2 0,0,A 0, 0<1. a) Suppose that the preferences of a consumer regarding the consumption of goods x1 and x2 are represented by function = f(x1,x2) above. Suppose also that the consumer is endowed with some disposable income Y > 0 and faces prices pı and p2 respectively for goods x1 and x2. i) Derive and describe the demand of the consumer for goods x1 and x2. [20 marks] i) Are demand functions affected...
iu [5 marks]b ii)) Consider the function, f, as the followings,vRuǐ (x1, x2)-5xỈ + x-. + 4x1 x2-14x1-6x2 + 20 ( !0% x») This function has its optimal solution atx"= (1,1) and f(1, 1) 10. Run the k-th iterates of the Newton algorithm, and compute the descend the k-th iteration (dk). [5 marks] Resource Allocation prob
iu [5 marks]b ii)) Consider the function, f, as the followings,vRuǐ (x1, x2)-5xỈ + x-. + 4x1 x2-14x1-6x2 + 20 ( !0% x») This...
Suppose that Jennifer produces good y by using input xi and x2. The production function which Jennifer faces is: y = x} + x3 The cost for every unit of xı is wi and the cost for every unit of x2 is w2. There is a fixed cost component F, which also forms a part of her total cost. (a) Write down the cost minimization problem. Solve this problem and express X1/X2 as a function of w2/w1.
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